Carsten Kengeter is on track to run Europe’s largest stock exchange. Three years ago, British prosecutors viewed him as a possible co-conspirator in the global interest-rate-rigging scandal.

Mr. Kengeter is chief executive of Deutsche Börse AG, the German exchange that is in talks to merge with London Stock Exchange Group PLC. Under terms of the planned merger, Mr. Kengeter would become CEO of the combined company, which will be...